The good, the bad, and the ugly witches

Our philofficer returns from vacation with this tidbit that appears to have emanated from George Takei’s Facebook page. The Star Trek icon posted this image of Glenda, the good witch from the Land of Oz.

Now, it takes someone like our philofficer to notice that the captions conceal a logical trap. People tend to think that “Only bad witches are ugly” means that you won’t find any pretty bad witches, when it really means you won’t find any ugly good witches — and there can be any number of pretty bad lovely bad ones.

Think about it this way: If it was your job to make sure the rule “Only bad witches are ugly” is being followed, you’d sort witches into “ugly” and “not ugly” groups and make sure no good witches make it into the “ugly” group. For your immediate purposes, it doesn’t matter how the witches in the “not ugly” group behave.

To get this right quickly, it helps to translate the original statement in the form “Only X’s are Y” into its logical equivalent, “No Y is not X” — that is, “No ugly witch isn’t bad.”

And, of course, if what you really meant to say was, “All bad witches are ugly” — well, just say so!